Goncharov's period-surjectivity conjecture for mixed Tate motives

Let $F$ be a number field, let ${\cal O}_{F,S}$ be a ring of $S$-integers, and let ${\cal A}_{\bullet}({\cal O}_{F,S})$ be its motivic Hopf algebra. Let ${\cal P}^{\sigma}_{\bullet}({\cal O}_{F,S})$ be the corresponding Hopf algebra of periods, and consider the surjective algebra homomorphism

$$p_{\sigma}:{\cal A}_{\bullet}({\cal O}_{F,S})\longrightarrow {\cal P}^{\sigma}_{\bullet}({\cal O}_{F,S}).$$

Goncharov's period-surjectivity conjecture. The map $p_{\sigma}$ is an isomorphism. Thus the expected upper bound on the dimensions of the period spaces is exact, meaning that the motivic periods account for all the relations among these periods.